Sorry to hear you are having problems with your build. While the hardware is not the best of choices, you certainly should be able to run that game at high settings with that hardware setup at that resolution and capped at 30fps for that game. So something hardware related is faulty.
My guess would be power supply or heat related.
I don't know if that PS is modular or not, but I know that power supply has 4 +12V rails. Two at 18A and two at 30A. Perhaps one of the rails is faulty or the system is unbalanced. You want to make sure you are using both of the 30A rails for the GPUs, one each. If you don't, then the PS will become unstable and give you unpredictable results.
The first thing I would try is pulling out one of the 4870's and try running it with a single GPU using the PCI-Express connector on one of the 30A rails. . If that doenst make a difference try using the other 30A rail.
I would think that should tell you if that is power supply related or not.
Otherwise, I think its a heat related issue. If the above doesnt work, swap out the one GPU you have in there with the 2nd one and try again. (that will also rule out a faulty GPU card). If that doesnt work then its not your GPU overheating or faulty card. It may be CPU overheating. Kind of a dumb question but you did use a thermal paste when you put the fan on the CPU, right? I'm sure you probably did but just being thorough
And all the fans are spinning everywhere, right?
Also double check your RAM sticks are in the correct slots (ie if you are only using 2 sticks and your board had 4 slots, make sure they are in the "correct slots" to take advantage of dual channel. If the 2nd RAM is in the wrong slot it may run single channel if your mobo allows.
Anyways give that a shot and let us know how it goes.